Before reverting
Consider carefully before reverting, as it rejects the contributions of another editor. In the edit summary or on the talk page, succinctly explain why the change you are reverting was a bad idea or why reverting it is a better idea. In cases of blatant vandalism, uncontroversially disruptive changes or unexplained removals the amount of explanation needed is minimal. But in the event of a content dispute, a convincing politely-worded explanation gains much importance and avoids unnecessary disputes.

Manual reverting
There are several ways to revert edits. A reversion can be carried out manually by editing the page to delete wrongly added text or restore wrongly deleted text. You can do this by copying and pasting text from a past version.
You can also restore a past version of the page. To do this:
Click the "View history" tab at the top of the page to display the page history.
Click the time and date of the earlier version to which you want to revert. You will see a phrase similar to: "This is an old revision of this page, as edited by User:Example (talk) at 15:47, January 24, 2018. It may differ significantly from the current revision."
Important: in the case of vandalism, take the time to make sure that you are reverting to the last version without the vandalism; there may be multiple consecutive vandal edits or they may be interspersed between constructive edits.
Click the "Edit" tab as you normally would. (Above the edit box, you will see a warning similar to: "You are editing an old revision of this page. If you save it, any changes made since then will be removed.") If editing requires a registered account, log in first, or go to the article's Talk page and ask a registered editor to take care of the matter.
Explain what you're doing in the edit summary field. Use complete words, not abbreviations. For example, "Reverting" or "Reverting vandalism."
Preview the page.
Publish changes.
Optional: Go to the Talk page and explain what you've done, and why.

Undo
For a past proposal to restrict the availability of this function because of potential misuse, see Wikipedia:Limit the undo function.
Shortcut
WP:UNDO
The MediaWiki software sometimes enables editors to easily revert (undo) a single edit from the history of a page, without simultaneously undoing all constructive changes that have been made since. To do this, view the page history or the diff for the edit, then click on "undo" next to the edit in question. The software will attempt to create an edit page with a version of the article in which the undesirable edit has been removed, but all later edits are retained. There is a default edit summary, but this can be modified before saving.
It is also possible to undo several consecutive edits, even if they conflict among themselves: view the "diff" to be removed (by selecting the earliest and most recent revisions in the history and clicking "compare selected revisions"), and click the "undo" link.

Rollback
See also: Wikipedia:Rollback
Administrators and other editors who have been granted access to the rollback feature have additional links that:
appear only next to the top edit
revert all top consecutive edits made by last editor
work immediately, without the intermediate confirmation diff page
add automatic edit summary "m Reverted edits by Example (talk) to last version by Example2", marking edit as minor
Rollback links appear on the user contributions pages, user watchlists, recent changes pages, history pages and diff pages. Note that in the last case, rollback links can be misleading, since reversion is not necessarily to the old version shown (the diff page may show the combined result of edits, including some by other editors or only part of the edits the rollback button would revert). To see the changes the rollback button will revert, view the specific diff that compares the last version from the last editor with the last version from the previous editor.
Rollback works much more quickly than undo, since it:
allows reverting without even looking at the list of revisions or diff
does not require loading an edit page and sending the wikitext back to the server
does not require a click of the Publish changes button
On the other hand, it is not as versatile as undo, since it does not allow specification of which edits have to be undone. One may want to revert more or less edits than the rollback does or edits that do not include the last edit. It also does not allow adding an explanation to the automatic edit summary. Rollback may only be used in certain circumstances; most commonly to revert obvious vandalism. Rolling back a good-faith edit or even during an edit-war may be interpreted as "I think your edit was no better than vandalism and reverting it doesn't need an explanation". The rollback right can be revoked on misuse: refer to its main page.
If someone else edited or rolled back the page before you clicked the "rollback" link, or if there was no previous editor, you will get an error message.
Bot rollback
In cases of flood vandalism (rapid changes to many articles), administrators may choose to hide vandalism and reverts from recent changes. To do this, add &bot=1 to the end of the url used to access a user's contributions. For example: http://en.wikipedia.org/w/index.php?title=Special:Contributions&target=SomePersistentVandal&bot=1.
When the rollback links on the contributions list are clicked, the revert and the original edit that you are reverting will both be hidden from recent changes, unless you click the "bots" link in the Recent Changes to set hidebots=0. The edits are not hidden from contributions lists, page histories or watchlists. The edits remain in the database and are not removed, but they no longer flood "Recent changes". The aim of this feature is to reduce the annoyance factor of a flood vandal, with relatively little effort. This should not be used for reverting a change you just don't like, but is meant only for massive floods of simple vandalism.

Reverting images
To revert an image to a previous version, go to the image page and click on "File history."
You will then see a list of past edits and a thumbnail graphic of each. Logged-in users will also see a "Revert" link for versions other than the current one. Click on a Revert link to make the change.
If the image is at Wikimedia Commons you must click through to the image page there to do the revert. You will need to be logged in at Commons.

Reverting multiple non-contiguous edits
Ultimately, it is the responsibility of the person reverting edits on the page to be sure that any intervening helpful edits are not reverted, or are re-applied to the article.
In some instances it is possible to progressively undo changes starting from the most recent and working backwards in time skipping those edits which are not to be reverted. The success of being able to do this will depend on where the various edits are located within the article text. If they overlap, or are close together within the text, the software will consider them to be conflicting with more recent edits and not permit an "undo" operation. In some cases it is easier to begin with this technique as it may revert at least some of the unhelpful edits providing a point from which it is easier to begin hand editing.
When considering reverting multiple edits, one should examine all of the intervening edits. These are often a mix of both helpful and unhelpful edits. The goal is to remove the effect of the unhelpful edits and leave the helpful ones. This can be done either by undoing the unhelpful edits or reverting to a version of the page prior to the beginning of the unhelpful edits and re-applying, by hand, the helpful edits. To re-apply helpful edits, or revert unhelpful edits, it is usually easier to copy-and-paste portions of a version of the article which contains, or does not contain those edits. In complex situations, this may result in combining portions of text from multiple versions of the article. The choice of starting this process from the current version as your base text, or using a prior version as your base will depend on the relative extent and localization within the article text of the changes which are to be kept and those to be reverted. It is usually easier to have the by-hand operation be on localized areas of text rather than those changes spread throughout an article. This can be a long (hours) and complex process. It can be quite helpful to use the "Show changes" button in the edit window to compare the current diff against a diff, in a different tab or window, of the changes which you are attempting to remove or re-apply.
If you are re-applying edits by other editors, you should state the original author(s) and which edit(s) in your edit summary to provide appropriate credit. If you are reverting to a prior version with the intent of re-applying changes in followup edits, you should explicitly say so in the edit summary of your reversion and use the {{in use}} template to indicate to other editors that you are working on the article. This is particularly important because the editors responsible for any edits which you have reverted will immediately be notified that their edit has been reverted. If there is no indication that you are working on the article, particularly if you are working to re-apply helpful edits, the other editors may edit the article in the intervening time creating an edit conflict. Having an edit reverted can be upsetting to other editors, particularly if considerable time and effort was put into performing the edit, if you are planning to re-apply such edits it is best to let the editors know that up-front.
The choice of method to use in complex situations is often based on your experience with the process and the available tools. Keep in mind that if you get into a situation which you find difficult to resolve, it is always possible to completely revert your own edit(s) and return the article to the condition in which you found it.

Additional tools
This page is referenced in the Wikipedia Glossary.
Sam Hocevar's godmode-light.js script adds functionality similar to the admin rollback links described above. More info at http://sam.zoy.org/wikipedia/.
Vandal edits can also be reverted using Popups, Huggle, Igloo, STiki, or Twinkle.